Chapter 11.6, Problem 50PPS

(a)

To determine

To calculate: The time taken by the boat to travel $6$ miles upstream and $3$ miles downstream.

Answer to Problem 50PPS

The required time to travel $4$ miles is $35$ .

Explanation of Solution

Given information:

The distance the boat travelled upstream is $6$ miles

The distance the boat travelled downstream is $3$ miles

Formula used:

Formula for time:

  $time=\frac{dis\tan ce}{speed}$

Calculation:

Consider the equation of speed, time and distance.

  $time=\frac{dis\tan ce}{speed}$

Substitute $6$ for distance and $x-2$ for time to find the time to travel upstream.

  $t_{up}=\frac{6}{x-2}$

Substitute $3$ for distance and $x+2$ for time to find the time to travel downstream.

  $t_{down}=\frac{3}{x+2}$

Add the time for upstream and downstream to calculate the total time.

  $t=\frac{6}{x-2}+\frac{3}{x+2}$

Hence the required expression of time is $t=\frac{6}{x-2}+\frac{3}{x+2}$